Linear Algebra 1 - Complete Notes

Notes on methods of solving systems of linear equations (or simultaneous equations including the Gauss Elimination Method.

Notes defining vector spaces and linear combinations for linear algebra. Includes all theorems required for the module section as well as examples and diagrams.

Notes on the Cayley-Hamilton Theorem in Linear Algebra with its corollary and a rigorous proof.

Definitions of rank and minors of a matrix with all associated theorems needed for this section of Linear Algebra 1.

Notes on how to find the determinant of an nxn matrix. Includes a number of theorems related to the determinant of a matrix as well as the effects of the determinant under elementary operations.

Notes covering the rules of matrix algebra including the elementary operations, transposition and inverting a matrix.

Notes on how to find the eigenvalues and eigenvectors of a matrix as well as how to determine whether a matrix is diagonalisable.